How does this formula that calculates CPU utilization work?
I've been given this question
Consider a system running ten I/0-bound tasks and one CpU-bound task. Assume that the I/O-bound tasks issue and I/O operation once for every millisecond of CPU computing and that each I/O operation takes 10 milliseconds to complete. Also assume that the context-switching overhead is .1 millisecond and that all processes are long running tasks Describe the CPU utilization for round-robin scheduler when:
a. The time quantum is 1 millisecond
b. The time quantum is 10 milliseconds
and I found answer for it
The time quantum is 1 millisecond: Irrespective of which process is scheduled, the scheduler incurs a 0.1 millisecond context-switching cost for every context-switch. This results in a CPU utilization of 1/1.1 * 100 = 91%.
The time quantum is 10 milliseconds: The I/O-bound tasks incur a context switch after using up only 1 millisecond of the time quantum. The time required to cycle through all the processes is therefore 10*1.1 + 10.1 (as each I/O-bound task executes for 1millisecond and then incur the context switch task, whereas the CPU- bound task executes for 10 milliseconds before incurring a context switch). The CPU utilization is therefore 20/21.1 * 100 = 94%.
My only question how is this person deriving the formula for CPU Utilization? I can't seem to under stand where he/she is getting the numbers 20/21.1 * 100 = 94%, and 1/1.1 * 100 = 91%.
Answer
For the first case, every task uses 1msec to do work and .1msec to switch; thus, it is spending 1 of every 1.1 msec doing work.
For the second case, it is similar: of the 21.1 msec spent to go through all tasks, only 20 of that is doing actual work.